I am using AIC as a model selection criteria in one of my projects. However, since AIC isn't dependent on the number of points sampled, for large n the log likelihood term rapidly outscales the parameter penalty.
I was wondering why the parameter penalty doesn't scale with the number of points, as the log likelihood generally does. It's getting to where the log likelihood is in the order of tens of thousands and the AIC penalty for having ~10 extra parameters in the model doesn't matter. But it feels like it really should. Am I misunderstanding something?